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    Simultaneous Diophantine approximation in the real, complex and p–adic fields


    Budarina, Natalia and Dickinson, Detta and Bernik, Vasili (2010) Simultaneous Diophantine approximation in the real, complex and p–adic fields. Mathematical Proceedings of the Cambridge Philosophical Society, 149 (2). pp. 193-216. ISSN 1469-8064

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    Abstract

    In this paper it is shown that if the volume sum ∑r = 1∞ Ψ(r) converges for a monotonic function Ψ then the set of points (x, z, w) ∈ ℝ × ℂ × ℚp which simultaneously satisfy the inequalities |P(x)| ≤ H−v1 Ψλ1(H), |P(z)| ≤ H−v2 Ψλ2(H) and |P(w)|p ≤ H−v3 Ψλ3(H) with v1 + 2v2 + v3 = n − 3 and λ1 + 2λ2 + λ3 = 1 for infinitely many integer polynomials P has measure zero.

    Item Type: Article
    Additional Information: Cite as: BUDARINA, N., DICKINSON, D., & BERNIK, V. (2010). Simultaneous Diophantine approximation in the real, complex and p–adic fields. Mathematical Proceedings of the Cambridge Philosophical Society, 149(2), 193-216. doi:10.1017/S0305004110000162
    Keywords: Simultaneous Diophantine approximation; real, complex and p–adic fields;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 10110
    Identification Number: https://doi.org/10.1017/S0305004110000162
    Depositing User: Dr. Detta Dickinson
    Date Deposited: 16 Oct 2018 16:38
    Journal or Publication Title: Mathematical Proceedings of the Cambridge Philosophical Society
    Publisher: Cambridge University Press
    Refereed: Yes
    URI:

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